An investor borrows a principal of 1,000,000 and agrees to an interest-only repayment at a rate...

 

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An investor borrows a principal of £1,000,000 and agrees to an interest-only repayment at a rate of 5% p.a., in equal quarterly installments, paid in arrears for 10 years. After 10 years the principal is paid back with a lump payment. The investor uses part of the principal to buy £200,000 nominal of 10-year government bonds, paying semi-annual coupons at a rate of 4% p.a. and producing a yield of 3.5% p.a. effective. Bonds are redeemed at par after 10 years. The remaining portion of the principal (denoted by P) is used to purchase properties that produce annual rental income at a rate of 4% of their initial value P for the first 5 years and, subsequently, at a rate of 5% of their initial value P. Rent is payable monthly in advance. (a) (4 marks) Let iL 4% p.a. be the annual effective rate applied to liabilities. Evaluate the present value at time zero of the total liability. - (b) (4 marks) Compute the present value at time zero of the portion of principal invested in bonds and deduce the investment in properties P. (c) (2 marks) Find the monthly rental income for the first five years and for the subsequent years. (d) (4 marks) Assume that rent and coupon payments are credited to a savings account that accrues interest at a rate i = 3% p.a. effective. What is the present value at time zero of the total savings invested for the 10 years? (e) (5 marks) After 10 years the bonds are redeemed and the properties sold and the resulting income is deposited in the same savings account as in (d). What is the minimum sale price for the properties to ensure that the project's net present value is non-negative? (f) (6 marks) Assume that the properties are sold after 10 years for £900,000. What is the vield of the proiect? An investor borrows a principal of £1,000,000 and agrees to an interest-only repayment at a rate of 5% p.a., in equal quarterly installments, paid in arrears for 10 years. After 10 years the principal is paid back with a lump payment. The investor uses part of the principal to buy £200,000 nominal of 10-year government bonds, paying semi-annual coupons at a rate of 4% p.a. and producing a yield of 3.5% p.a. effective. Bonds are redeemed at par after 10 years. The remaining portion of the principal (denoted by P) is used to purchase properties that produce annual rental income at a rate of 4% of their initial value P for the first 5 years and, subsequently, at a rate of 5% of their initial value P. Rent is payable monthly in advance. (a) (4 marks) Let iL 4% p.a. be the annual effective rate applied to liabilities. Evaluate the present value at time zero of the total liability. - (b) (4 marks) Compute the present value at time zero of the portion of principal invested in bonds and deduce the investment in properties P. (c) (2 marks) Find the monthly rental income for the first five years and for the subsequent years. (d) (4 marks) Assume that rent and coupon payments are credited to a savings account that accrues interest at a rate i = 3% p.a. effective. What is the present value at time zero of the total savings invested for the 10 years? (e) (5 marks) After 10 years the bonds are redeemed and the properties sold and the resulting income is deposited in the same savings account as in (d). What is the minimum sale price for the properties to ensure that the project's net present value is non-negative? (f) (6 marks) Assume that the properties are sold after 10 years for £900,000. What is the vield of the proiect?

Answer rating: 100% (QA)

a The present value of the total liability at time zero is 18261538 b The present value of the porti... View the full answer